Cats should be taught to be handled from a young age. This includes picking him up, handling his paws and trimming the nails and getting used to having himself examined including checking inside the ears and mouth.
From time to time, you will need to pick up your cat. It may be to remove him from a dangerous situation or pick him up and put him into a cat carrier. There are right and wrong ways to do this.
How to pick up a cat:
Approach him from the side or front so that he can see and hear you. Talk to him quietly and give him a stroke.
Slide one arm underneath your cat's belly, and pick him up, supporting the hind legs and body on your arm (I'm right handed and use my left hand for this).
Pull him close to your chest. Wrap your other arm (in my case, my right arm) around the front part of his body with his front legs resting on your arm. So you have one arm under the rear of his body and legs, and the other arm wrapped around the front and side of his body, holding him close to you and supporting the front legs.
If you have a friendly and relaxed cat (as I do), he may prefer to slide around so that his front legs are resting on your shoulder. This is generally okay if you are in a safe environment such as at home, but if you are in an unpredictable environment, for example, the veterinarian's office, I wouldn't recommend this. Just because he is close to your face and unrestrained, he may accidentally scratch you if he becomes scared or leaps out of your arms. So only ever do this in a calm and relaxed environment.
What not to do:
As we've already said, don't pick up a cat by the scruff of the neck.
Don't pick up a cat by the tail.
Don't pick up a cat by the legs.
Supervise children with cats. They should only hold a cat if they are sitting down.
Scruffing a cat:
You should not pick up a cat over a few months of age by the scruff of the neck. Yes, this is now mother cats pick up and move her kittens, but they are small and light. A fully grown cat can range in weight from 4kg to 8kg and picking up by the scruff without providing additional support is going to place enormous strain on the spine and muscles.
Scruffing a cat can be used to restrain him, but it is best to do this on a supportive surface. Examples are when your cat is at the veterinarian. Scruffing doesn't hurt your cat but it does help to immobilise him. Another time you may want to scruff him is if you are trying to medicate him. One person holds him and scruffs, the other person administers medication. This should only be done as a last resort with a cat who is showing resistance.
Children handling cats:
Cats and children can be a great combination but there is always the potential for the cat or the child to get hurt if children don't follow basic safety precautions. A cat is quite heavy to a young child and they should not be allowed to pick up a cat until they are physically strong enough to do so safely. If handled incorrectly a cat can and will lash out and scratch or bite. There is also potential for the cat to become injured. So wait until your child is older and teach him how to pick up a cat safely, and only when necessary.
One more precaution. Don't pick up a cat to remove him from a fight. This may sound like the logical approach but a wound up cat can be dangerous and unintentionally lash out. If you encounter your cat fighting, get a broom and split them up that way.